ok, here's the problem.. prove <u,v> = 0 iff ||u|| less than or equal
to ||u + av||
where u,v in V and a is in F.
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so, <u,v> = 0 iff <v, u> = 0
squaring both sides ||u|| ^2 = ||u|| ^2 + |a|^2 ||v||^2
= <u + av, u + av>
= <u, u> + a <v,v> + .....?
it is a simple problem, and any pointers to solution will be
appreciated.
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